Abstract
INTRODUCTION
Understanding bone morphology is essential for successful computer assisted orthopaedic surgery, where definition of normal anatomical variations and abnormal morphological patterns can assist in surgical planning and evaluation of outcomes. The proximal femur was the anatomical target of the study described here. Orthopaedic surgeons have studied femoral geometry using 2D and 3D radiographs for precise fit of bone-implant with biological fixation.
METHOD
The use of a Statistical Shape Model (SSM) is a promising venue for understanding bone morphologies and for deriving generic description of normal anatomy. A SSM uses measures of statistics on geometrical descriptions over a population. Current SSM construction methods, based on Principal Component Analysis (PCA), assume that shape morphologies can be modeled by pure point translations. Complicated morphologies, such as the femoral head-neck junction that has non-rigid components, can be poorly explained by PCA. In this work, we showed that PCA was impotent for processing complex deformations of the proximal femur and propose in its place our Principal Tangent Component (PTC) analysis. The new method used the Lie algebra of affine transformation matrices to perform simple computations, in tangent spaces, that corresponded to complex deformations on the data manifold.
RESULTS
Both PCA and PTC were applied to the proximal femur dataset, from which selected femurs were reconstructed using the accumulation of components. PCA was deemed to have failed to reconstruct the surfaces because it required 65 components to achieve high coverage of the dataset. An important observation was that the head-neck junction was the most difficult section in the femur, requiring more components than other anatomical regions to reconstruct. This finding is consistent with the surgical observation that deformations occur in this junction for abnormal hip morphologies.
PTC was successful in recovering 100% of the medical data using the only the first 5 components. We note that the encoding of deformation in PTC accounting for the performance increase. PTC outperformed PCA on the dataset in descriptive compactness.
CONCLUSION
A standard SSM construction method was not adequate for analysing proximal femur surfaces because it could not easily model the complexity of non-rigid deformations at the head-neck junction. Principal tangent components, a novel method for using exponential maps on manifolds, accurately reconstructed the anatomical surfaces with very few components. Future work may include extending these concepts to describe joint diseases based on the shape of surfaces derived from volumetric data, such as CT or MRI. In conclusion, we have shown that differential geometry may be provide new insights to computational anatomy applications.
